Axiom Definition And Meaning: What is an Axiom?

Definition of Axiom

axiom [ˈæksɪəm]


  • (Mathematics) a generally accepted proposition or principle, sanctioned by experience; maxim

  • a universally established principle or law that is not a necessary truth the axioms of politics

  • (Philosophy / Logic) a self-evident statement

  • (Philosophy / Logic) (Mathematics) Logic maths a statement or formula that is stipulated to be true for the purpose of a chain of reasoning: the foundation of a formal deductive system Compare assumption

  • A self-evident or universally recognized truth; a maxim: "It is an economic axiom as old as the hills that goods and services can be paid for only with goods and services" (Albert Jay Nock).

  • An established rule, principle, or law.

  • A self-evident principle or one that is accepted as true without proof as the basis for argument; a postulate.


n. A self-evident, undemonstrable, theoretical, and general proposition to which every one who apprehends its meaning must assent. The Greek word was probably applied by Plato (though it does not occur in his dialogues in this sense) to certain first premises of mathematics; and this continues to be the ordinary use of the term. It was extended by Aristotle to similar principles supposed to underlie other branches of knowledge. The axioms or “common notions” of Euclid, as given in English translations, are twelve in number, viz.:

n. Any higher proposition, obtained by generalization and induction from the observation of individual instances; the enunciation of a general fact; an empirical law. This use originated with Bacon, influenced probably by the employment of axiom by the Stoics to mean any proposition.

n. In logic, a proposition, whether true or false: a use of the term which originated with Zeno the Stoic. Synonyms Maxim, Truism, etc. See aphorism.

n. one of those generalizations of ordinary experience which nobody doubts, and which are soon replaced by scientific formulations, which latter are also, but less properly, termed middle axioms.

Axiom Meaning and Explanation

An axiom is an assumption that is assumed to be true in some mathematical system. The axioms of geometry are historically called postulates. Intuitively an axiom is a statement whose truth is self-evident. Mathematical axioms need not be self-evident or true in any real-world sense. An axiom of one mathematical system may be false in a different system.
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